The brainstem reticular formation is a small-world, not scale-free, network

Recently, it has been demonstrated that several complex systems may have simple graph-theoretic characterizations as so-called ‘small-world’ and ‘scale-free’ networks. These networks have also been applied to the gross neural connectivity between primate cortical areas and the nervous system of Caenorhabditis elegans. Here, we extend this work to a specific neural circuit of the vertebrate brain—the medial reticular formation (RF) of the brainstem—and, in doing so, we have made three key contributions. First, this work constitutes the first model (and quantitative review) of this important brain structure for over three decades. Second, we have developed the first graph-theoretic analysis of vertebrate brain connectivity at the neural network level. Third, we propose simple metrics to quantitatively assess the extent to which the networks studied are small-world or scale-free. We conclude that the medial RF is configured to create small-world (implying coherent rapid-processing capabilities), but not scale-free, type networks under assumptions which are amenable to quantitative measurement

Seashore disturbance and management of the clonal Arctophila fulva : Modelling patch dynamics

Question: What is the population viability of a critically endangered seashore grass, Arctophila fulva var. pendulina. Location: Liminka Bay, W Finland, 25°21'70 N, 64°51'90 E. Methods: We constructed a matrix population model based on colonization and disappearance events and patch size changes of A. fulva. Patches were divided into hydric and nonhydric zones according to proximity to the seashore and intensity of disturbance. Perturbation analyses were carried out in order to identify transitions critical for population growth. Seed bank and seed germination studies provided background information for the model design. Results: A. fulva patches observed in the more disturbed hydric zone (closest to the sea) increased in number, as did the total number of patches. However, the number of patches in the less disturbed non-hydric zone decreased. Conclusions: Short-term dynamics of the A. fulva population at Liminka Bay seem to be determined by environmental fluctuations, which cause annual variation in transition rates between patch size classes. The long-term dynamics are probably governed by initiation of primary succession by isostatic land uplift. Increased disturbance at the water’s edge may promote persistence of A. fulva through reduced interspecific competition. Our results suggest that shoreline disturbance of the hydric zone is sufficient for maintaining a viable population. Competitive exclusion of A. fulva in the non-hydric zone may be delayed by management practices, such as mowing

On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle (Part One)

In October 1924, the Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck combined advanced techniques of classical mechanics with Bohr's correspondence principle and Einstein's quantum theory of radiation to find quantum analogues of classical expressions for the emission, absorption, and dispersion of radiation. For modern readers Van Vleck's paper is much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg's "Umdeutung" paper. This makes Van Vleck's paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself.Comment: 82 page